The simulation of complex systems is important in many fields of science and in real-world
applications. Such systems are composed of many interacting subsystems. There might
exist different software packages for simulating the individual subsystems and co-simulation
refers to the simultaneous execution of multiple interacting subsystem simulators.
Simulation or co-simulation, if not designed properly, can return misleading numerical
solutions (unstable numerical solutions for what is in fact a stable system or vice
versa). To understand the cause of these numerical artifacts, we first propose a simple
mathematical model for co-simulation, and then construct stability charts. These charts
shed light on transitions between stable and unstable behavior in co-simulation. Our
goal is to understand the stability properties of the simulated and co-simulated representation
of the continuous system. We will achieve this goal by expressing the trace and determinant
of the discretized system in terms of the trace and determinant of the continuous
system to establish stability criteria.